The construction of [1]} that we will describe address the above issues in two respects. First, it produces the Casimir equations for any kind four-point functions in theories with type I superconformal symmetry in terms of Casimir equations for appropriate spinning bosonic partial waves. This is possible due to the fact that under the map (REF ) the Casimir equations are carried to the eigenvalue problem for the Laplacian \(\Delta \)  on the space of \(K\) -spherical functions. In general, the expression for the Laplacian on a type I supergroup can be related to its bosonic counterpart \(\Delta _0\)  provided that one works in a particular coordinate system that we will introduce in the second subsection. In these coordinates, \(\Delta \)  differs from \(\Delta _0\)  by a nilpotent term \(A\)  and a simple “trace” term.
